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We present the HOLISMOKES programme on strong gravitational lensing ofsupernovae as a probe of supernova (SN) physics and cosmology. We investigatethe effects of microlensing on early-phase SN Ia spectra using four differentSN explosion models, and find that within 10 rest-frame days after SNexplosion, distortions of SN Ia spectra due to microlensing are typicallynegligible ($<$1% distortion within the 1$\sigma$ spread, and $\lesssim$10%distortion within the 2$\sigma$ spread). This shows great prospects of usinglensed SNe Ia to obtain intrinsic early-phase SN spectra for deciphering SN Iaprogenitors. As a demonstration of the usefulness of lensed SNe Ia forcosmology, we simulate a sample of mock lensed SN Ia systems that are expectedto have accurate and precise time-delay measurements in the era of the RubinObservatory Legacy Survey of Space and Time (LSST). Adopting realistic yetconservative uncertainties on their time-delay distances and lens angulardiameter distances (of 6.6% and 5%, respectively), we find that a sample of 20lensed SNe Ia would allow a constraint on the Hubble constant ($H_0$) with 1.3%uncertainty in the flat $\Lambda$CDM cosmology. We find a similar constraint on$H_0$ in an open $\Lambda$CDM cosmology, while the constraint degrades to $3\%$in a flat $w$CDM cosmology. We anticipate lensed SNe to be an independent andpowerful probe of SN physics and cosmology in the upcoming LSST era.

HOLISMOKES -- I. Highly Optimised Lensing Investigations of Supernovae, Microlensing Objects, and Kinematics of Ellipticals and Spirals